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United States Patent |
5,587,793
|
Nakai
,   et al.
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December 24, 1996
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Birefringence distribution measuring method
Abstract
A sample is placed between a circular polarizer and an analyzer in an
optical path between a monochromatic light source and a two-dimensional
optical receiver. Parallel beams emitted from the monochromatic light
source are converted into circularly polarized light by the circular
polarizer. After transmitting the sample, the light is guided to the
analyzer. While rotating the analyzer about the axis of the beams, image
data are detected by optical receiver at a step of a regular rotation
angle, and the detected image data are sampled to be sent to an image
processing device in the next stage. On the basis of the image data, an
operation is conducted on each pixel to obtain a relative phase difference
due to birefringence of the sample, the two-dimensional birefringence
distribution including the sign of the relative phase difference, and also
the principal axis direction.
Inventors:
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Nakai; Sadao (6-45, Kitakasugaoka 3-chome, Ibaragi-shi, Osaka, JP);
Izawa; Yasukazu (Suita, JP);
Yamanaka; Masanobu (Minoo, JP);
Ohmi; Masato (Toyonaka, JP);
Akatsuka; Masanori (Osaka, JP);
Yamanaka; Chiyoe (Osaka, JP);
Yonezawa; Yoshiyuki (Kawasaki, JP)
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Assignee:
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Nakai; Sadao (Osaka, JP);
Institute for Laser Technology (Osaka, JP);
Fuji Electric Co., Ltd. (Kanagawa, JP)
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Appl. No.:
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470157 |
Filed:
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June 6, 1995 |
Foreign Application Priority Data
Current U.S. Class: |
356/367 |
Intern'l Class: |
G01N 021/23 |
Field of Search: |
356/364,365,366,367,368
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References Cited
U.S. Patent Documents
5257092 | Oct., 1993 | Noguchi et al. | 356/367.
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Foreign Patent Documents |
60-29621 | Feb., 1985 | JP.
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Other References
"Solid-State Laser Engineering", Koechner, W., Third Completely Revised and
Updated Edition, pp. 393-394, 1992.
Masato Noguchi et al., "Measurement of 2-D Birefringence Distribution" SPIE
vol. 1720 (1992) pp. 367-378.
V. S. Chudakov, "Investigation of Induced Birefringence with a Rotating
Polarization Element" Instrum. & Exper. Techn. vol. 20, (1977) pp.
241-244.
Otani et al., "Two-dimensional Birefringence Measurement Using the Phase
Shifting Technique" SPIE vol. 1720, pp. 346-354 (1992).
Matsuura et al, "Measurement of flow-birefringence using a circularly
polarized laser beam". Optics and Laser Technology vol. 10, No. 5 (Oct.
1978) pp. 237-240.
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Primary Examiner: Rosenberger; Richard A.
Attorney, Agent or Firm: Finnegan, Henderson, Farabow, Garrett & Dunner, L.L.P.
Parent Case Text
This application is a continuation of application Ser. No. 08/149,811 filed
Nov. 10, 1993, now abandoned.
Claims
What is claimed is:
1. A birefringence distribution measuring method of two-dimensionally
measuring a birefringence distribution induced in a sample, comprising the
steps of:
placing said sample between a circular polarizer and an analyzer in an
optical path between a monochromatic light source and a two-dimensional
optical receiver;
converting a plurality of parallel beams emitted from said monochromatic
light source into circularly polarized light by said circular polarizer;
transmitting said circularly polarized light through said sample to said
analyzer;
detecting image data by said two-dimensional optical receiver while
rotating said analyzer about an axis of the plurality of beams, at a step
of a fixed rotation angle;
sampling said detected image data and sending the sampled data to an image
processing device; and
processing the sampled image data to obtain a relative phase difference due
to birefringence of said sample, a two-dimensional birefringence
distribution including the sign of said relative phase difference, and the
direction of the principal axis.
2. The method of claim 1, wherein said processing step includes the step of
fitting the sampled data to a curve defined by sin2(.phi.-.theta.) wherein
.phi. is the angle of the principal axis and .theta. is the angle between
the principal axis and the analyzer.
3. The method of claim 2, wherein said processing step further comprises
the step of measuring the phase difference due to birefringence at the
point where sin2(.phi.-.theta.)=1.
Description
BACKGROUND OF THE INVENTION
The invention relates to a birefringence distribution measuring method,
and, more particularly, it concerns such a method which obtains
quantitatively and two-dimensionally a birefringence distribution induced
when thermal or mechanical stress is produced in a laser medium of a solid
state laser represented by a YAG laser, for example.
A solid state laser, such as a YAG laser, begins laser oscillation when
energy from an excitation light source, such as a lamp, is applied to a
laser medium. A part of the lamp light is converted into heat and
accumulated in the laser medium so that a temperature gradient or
distortion is produced inside the laser medium. As is well known, this
causes the laser medium to have optical anisotropy, thereby allowing
birefringence to appear.
More particularly, when a temperature gradient is produced inside the laser
medium, the difference in thermal expansion between the surface and the
center of the medium makes the medium distort, thus generating internal
stresses. Similarly, mechanical stresses resulting from mounting the laser
medium causes internal stresses in the laser medium. The refractive index
of a medium for light depends on stress. As a result, a distribution of
refractive indices is produced inside the medium (photoelastic effect).
Also, the refractive index changes in accordance with the polarization
direction of light. The refractive index in the direction of the principal
axis is different from that of a direction perpendicular to the principal
axis, so that when linearly polarized light enters a birefringent
substance at an angle to the principal axis of stress produced in the
substance, the phase velocities in the two directions are differentiated
from each other. The resulting phase difference produces elliptically
polarized light. Further, two light beams of different vibration
directions progress in different velocities (birefringence) through the
birefringent substance. Of the two polarized waves due to birefringence,
one wave having one plane of vibration progresses more rapidly, and the
other wave progresses slowly. The two waves are called "fast wave" and
"slow wave", respectively.
In a solid state laser, a laser beam is amplified when it is reflected back
and forth between two mirrors. When birefringence due to the thermal or
mechanical stress has occurred inside the laser medium, therefore, the
relative phase difference between the two refracted beams causes the wave
front to be disturbed, thereby presenting an obstacle to effective laser
operation in cases where a laser beam emitted from a laser is output as
linearly polarized light and then amplified for use.
From the standpoint of promoting the study of birefringence compensation to
obtain a laser beam having a small wave front distortion, therefore, there
is a need for an improved method for measuring, two-dimensionally, a
birefringence distribution which obtains quantitatively and with high
sensitivity birefringence induced in a laser medium of a solid state
laser.
Typically, known methods for quantitatively measuring a two-dimensional
distribution of birefringence using a conoscope. FIGS. 3 and 4 show in
block diagram from systems representing the principle of the known
measuring method. In these figures, 1 designates a sample having a
birefringence effect (e.g., a crystal plate or glass plate which is to be
used as a laser medium of a solid state laser), 2 designates a
monochromatic light source (e.g., He-Ne laser), 3 designates an optical
receiver for guiding a received image to a screen, 4 designates a
polarizer, 5 designates an analyzer, and 6 and 7 designate quarter-wave
plates.
In FIG. 3, the sample 1 is placed between a circular polarizer (a
combination of the polarizer 4 and the quarter-wave plate 6) and a
circular analyzer (which is a combination of the quarter-wave plate 7 and
the analyzer 5 and which is arranged to establish crossed Nicols with
respect to the circular polarizer), and arranged in the optical path
between the light source 2 and the optical receiver 3. In the
configuration, monochromatic parallel beams emitted from the light source
2 are converted into circularly polarized light by the circular polarizer
and then projected onto sample 1. The light beams which have undergone
birefringence inside the sample 1 pass through the circular analyzer to be
detected by the optical receiver 3. When the light intensity after passing
through the polarizer 4 is I.sub.0, the light intensity detected by the
optical receiver 3 is indicated by I, the angle of the axis at a point in
the sample 1 which is formed by the vibration direction of the fast wave
passing through the sample and the principal plane of the analyzer 5 is
indicated by .phi., and the relative phase difference between the two
beams due to birefringence is indicated by .delta., as is well known, the
intensity distribution changes in proportion to the equation:
I=I.sub.0 sin.sup.2 (.delta./2) (1)
In the configuration of FIG. 4 which is the same as that of FIG. 3 except
that the quarter-wave plates 6 and 7 are omitted, the intensity
distribution changes in proportion to the equation:
I=I.sub.0 sin.sup.2 (2.phi.).times.sin.sup.2 (.delta./2) (2)
In the configuration of FIG. 4, therefore, the intensity distribution of
the intensity of the beams passing through the sample 1 and detected by
the optical receiver 3 is measured. The direction in which the intensity
is zero (I=0) indicates the direction of the principal axis (angle .phi.).
From the intensity to this direction, the relative phase difference 6 can
be calculated in accordance with Eq. (2). In the configuration of FIG. 3,
the information relating to the direction principal axis is lost, and
therefore only the relative phase difference .delta. is obtained.
As seen from Eqs. (1) and (2) above, according to the birefringence
distribution measuring method using a conoscope, it is possible to obtain
the absolute value of the relative phase difference .delta. between two
refracted beams due to birefringence, and also the two-dimensional
distribution of birefringence, but it is impossible to determine the sign
of the relative phase difference .delta.. Further, in Eqs. (1) and (2)
above, the relative phase difference .delta. is presented in the term of a
second degree, sin.sup.2 (.delta./2). Therefore, when the relative phase
difference .delta. is very small, for example, less than .pi./4 radians,
the term of sin.sup.2 (.delta./2) is approximated to be .delta..sup.2 /4,
resulting in impaired measurement sensitivity.
As described above, the prior art measuring method cannot judge the sign of
the relative phase difference .delta.. In the state of the art, a simple
method of two-dimensionally measuring a birefringence distribution which
can obtain both the sign of the relative phase difference and the
principal axis direction has not yet been put to practical use.
SUMMARY OF THE INVENTION
The invention has been made in view of the above, and has an objective of
providing a novel birefringence distribution measuring method which can
measure quantitatively and with high sensitivity a two-dimensional
distribution of birefringence induced in a sample, including the sign of
the relative phase difference, and obtain the principal axis direction.
Additional objects and advantages of the invention will be set forth in
part in the description which follows and in part will be obvious from the
description, or may be learned by practice of the invention. The objects
and advantages of the invention may be realized and attained by means of
the instrumentalities and combinations particularly pointed out in the
appended claims.
In order to accomplish the objectives, according to the birefringence
distribution measuring method of the invention, the sample is placed
between a circular polarizer and an analyzer which are in an optical path
between a monochromatic light source and a two-dimensional optical
receiver; parallel beams emitted from the monochromatic light source are
converted into circularly polarized light by the circular polarizer; and
the circularly polarized light is passed through the sample and then to
the analyzer. The image data are detected by the optical receiver while
rotating the analyzer about an axis of the beams, at a step of a fixed
rotation angle; the detected image data are sampled and the sampled data
are sent to an image processing device. The sampled image data are then
processed in the unit of a pixel to obtain a relative phase difference due
to birefringence of the sample, a two-dimensional birefringence
distribution including the sign of the relative phase difference, and the
direction of the principal axis.
When a birefringence distribution of a sample is measured in the
above-mentioned arrangement of optical devices or the laser medium is
distorted by, for example, irradiating with light (corresponding to the
excitation lamp light for a laser) so that the laser medium has optical
anisotropy, the intensity, I, of light which has passed through the
circular polarizer, the sample, and the circular analyzer is given by the
following equation:
I=(I.sub.0 /2).times.(1.+-.sin2.phi..times.sin.delta.) (3)
where I.sub.0, .phi. and .delta. are the same as those used in above
equations (1) and (2). In the equation, the symbol .+-. indicates the
rotation direction of circularly polarized light (right-handed direction
or left-handed direction). In the case where right-handed circularly
polarized light is employed, Eq. (3) above is written as:
I=(I.sub.0 /2).times.(1+sin2.phi..times.sin.delta.) (4)
When the principal axis direction is inclined in a counterclockwise
direction at an angle .theta. to the principal plane of the analyzer, the
Eq. (4) is written as:
I=(I.sub.0 /2).times.[1.+-.sin2(.phi.-.theta.).times.sin.delta.]tm (5)
As seen from Eq. (5), in the state where birefringence has not occurred in
the sample, I is equal to I.sub.0 /2. In contrast, when a birefringence
distribution is to be measured in the state where refraction is induced by
producing thermal or mechanical stresses in the sample, parallel beams
emitted from the monochromatic light source are converted into circularly
polarized light by the circular polarizer and then guided through the
sample to the analyzer. In this state, the analyzer is rotated by from
angle of 0 to 180 degrees about the optical axis, and, for example, seven
sets of image data which are detected by the two-dimensional optical
receiver at a step of 30 degrees are sampled. The sampled image data are
sent to an image processing device in the next stage and stored therein.
On the basis of the image data, the image processing device conducts the
operation described below on each of the pixels. First, the curve of
sin2(.phi.-.theta.) is fitted to each of the pixels of the image data,
and, at the position where sin2(.phi.-.theta.)=1, the vibration direction
(principal axis direction) of the fast wave among the two polarized waves
due to birefringence is obtained. Under the conditions at this time, the
relative phase difference .delta. between the fast wave and the slow wave
is calculated from sin.delta. in the above equation, together with the
judgment of the sign of the relative phase difference .delta.. Then, the
image processing device conducts these processes on each of the pixels of
the image data, whereby both the two-dimensional distribution of
birefringence in the sample and the principal axis direction can be
measured simultaneously.
As seen from Equations (3) to (5) above, the relative phase difference
.delta. is presented in a term of the first power, sin.delta.. Therefore,
when the relative phase difference .delta. is very small or less than
.pi./4 radians the term of sin.delta. is approximated to .delta.,
resulting in that even a minute of relative phase difference .delta. can
be measured with high sensitivity.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part
of this specification illustrate an exemplary embodiment of the invention
and, together with the description, serve to explain the objects,
advantages and principles of the invention. In the drawings,
FIG. 1 is a diagram showing the configuration of a two-dimensional
birefringence measuring device according to an embodiment of the
invention;
FIG. 2 is a view showing, in the form of a graph a simulation of an example
of measuring, a birefringence distribution in accordance with the device
of FIG. 1;
FIG. 3 is a diagram showing the configuration of a prior art birefringence
measuring device; and
FIG. 4 is a diagram showing the configuration of another prior art
birefringence measuring device.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Hereinafter, an embodiment of the invention will be described with
reference to FIG. 1. In the figure, components corresponding to those of
FIGS. 3 and 4 are designated by the same reference numerals.
In the configuration of FIG. 1, a sample 1 having a birefringence effect is
placed between a circular polarizer 9 which is a combination of a
polarizer 4 and a quarter-wave plate 6, and an analyzer 5 in an optical
path between a monochromatic light source 2 (e.g., He-Ne laser
(wavelength: 632.8 nm)) and a two-dimensional optical receiver 8 (e.g., an
image pickup device such as a charge coupled device (CCD) camera). The
analyzer 5 is provided with a driving mechanism 10 for rotating the
analyzer about the optical axis. The two-dimensional optical receiver 8 is
connected to an image processing device (computer) 11.
In this configuration, the principal axis of the quarter-wave plate 6 is
previously selected, and the rotation direction of circularly polarized
light is set to be either the right-handed direction or left-handed
direction. During the measurement, monochromatic parallel beams emitted
from the light source 2 are converted into circularly polarized light by
the circular polarizer 9. After passing through the sample 1, in which
birefringence is induced, and the analyzer 5, the light is detected by the
two-dimensional optical receiver 8. In the embodiment, the driving
mechanism 10 operates so as to rotate the analyzer 5 from an angle of 0 to
180 degrees about the optical axis. In synchronization with the rotation
angle, the two-dimensional optical receiver 8 outputs seven sets of image
data at a regular angle step of, for example, 30 degrees, and the image
data are stored in the image processing device 11. Then, according to
Equations (3) to (5) above, the image processing device 11 conducts
predetermined operations on each of the pixels of the stored image data,
to calculate the relative phase difference .delta. at each point of sample
1 in which birefringence is induced, the sign of the relative phase
difference, and the principal axis direction, thereby quantitatively
obtaining the two-dimensional distribution of birefringence.
FIG. 2 shows, in the form of a graph, a simulation of a measurement example
according to the above-described measuring method. In this example, on the
assumption that the relative phase difference .delta. is +.pi./2, the
principal axis direction .theta. and the relative phase difference .delta.
are calculated according to Eq. (5) from imaged data obtained in a
measurement. In the figure, the solid line indicates the case of .theta.=0
degrees and the broken line the case of .theta.=45 degrees. The points at
which an image obtained by further rotating the analyzer 5 by 30 degrees
about the optical axis is input to the image processing device 11 are
indicated on the curves by open circles, respectively.
The computer of the image processing device 11 conducts the curve-fitting
so that (I.sub.0 /2)[1+sin2(.phi.-.theta.).times.sin.delta.] is fitted to
each of the open circles, thereby obtaining the curve indicated by the
solid line (or the broken line). At the points on the solid line (or
broken line) curve where [1+sin2(.phi.-.theta.).times.sin.delta.]/2 is 1,
sin.delta. is +1. From this, it is known that .delta. is equal to +.pi./2.
As a result of the curve-fitting, the principal axis direction is found to
be 0 or 45 degrees. This operation is executed on each of the pixels of
the image data, so that the two-dimensional distribution of birefringence
is obtained.
As described above, according to the birefringence distribution measuring
method of the present invention, a two-dimensional distribution due to
birefringence, including the sign of the relative phase difference, and
also the principal axis direction can be measured quantitatively and with
high sensitivity from a sample such as a solid state laser material in
which birefringence is induced by thermal or mechanical stress.
The foregoing description of preferred embodiments of the invention has
been presented for purposes of illustration and description. It is not
intended to be exhaustive or to limit the invention to the precise form
disclosed, and modifications and variations are possible in light of the
above teachings or may be acquired from practice of the invention. The
embodiment was chosen and described in order to explain the principles of
the invention and its practical application to enable one skilled in the
art to utilize the invention in various embodiments and with various
modifications as are suited to the particular use contemplated. It is
intended that the scope of the invention be defined by the claims appended
hereto, and their equivalents.
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